My dictionary says the word 'home' in the above sentence is an adverb ... but why? My grammar says adverb has 3 functions: to modify verbs, to modify adjectives, and to modify adverbs. I thought 'home' here modifies 'Sue' which is a noun. Isn't it an adjective instead?

No, it does not modify anything here: it complements the copula 'is' and does indeed function as an adverb. (As a simple check, note that the word 'home' here specifies simply WHERE Sue is - an adverbial function - and not what she is like!)